Some results for cyclic weak contractions in modular metric space
محورهای موضوعی : Fixed point theory
H. Rahimpoor
1
(Department of Mathematics, Payame Noor University, Tehran, Iran)
I. Nikoufar
2
(Department of Mathematics, Payame Noor University, Tehran, Iran)
کلید واژه: fixed point, modular metric space, convex modular, cyclic $\phi$-contraction,
چکیده مقاله :
In this paper, we present some fixed point results for cyclic weak $\phi$-contractions in $\omega$-complete modular metric spaces and $\omega$-compact modular metric spaces, respectively. Some results for contractions that have zero cyclic properties are also provided.
[1] C. Alaca, M. E. Ege, C. Park, Fixed point results for modular ultrametric spaces, J. Comput. Anal. Appl. 20 (7) (2016), 1259-1267.
[2] V. V. Chystyakov, Modular metric spaces generated by F-modulars, Folia Math. 15 (2008), 3-24.
[3] V. V. Chystyakov, Modular metric spaces I: Basic concepts, Nonlinear Anal. 72 (2010), 1-14.
[4] V. V. Chystyakov, Modular metric spaces II: Application to superposition operators, Nonlinear Anal. 72 (2010), 15-30.
[5] M. E. Ege, C. Alaca, Fixed point results and an application to homotopy in modular metric spaces, J. Nonlinear Sci. Appl. 8 (6) (2015), 900-908.
[6] M. E. Ege, C. Alaca, Some properties of modular S-metric spaces and its fixed point results, J. Comput. Anal. Appl. 20 (1) (2016), 24-33.
[7] M. E. Ege, C. Alaca, Some results for modular b-metric spaces and an application to system of linear equations, Azerb. J. Math. 8 (1) (2018), 3-14.
[8] A. Gholidahneh, S. Sedghi, O. Ege, Z. D. Mitrovic, M. De la Sen, The Meir-Keeler type contractions in extended modular b-metric spaces with an application, AIMS Math. 6 (2) (2021), 1781-1799.
[9] H. A. Hammad, R. A. Rashwan, A. H. Ansari, C-class functions on common fixed point theorems for weak contraction mapping of integral type in modular spaces, J. Linear. Topological. Algebra. 8 (4) (2019), 265-285.
[10] J. Harjani, B. Lopez, K. Sadarangani, Fixed point theorems for cyclic weak contractions in compact metric spaces, J. Nonlinear Sci. Appl. 6 (2013), 279-284.
[11] H. Hosseini, M. Eshaghi Gordji, Best proximity point theorems in 1/2-modular metric spaces, J. Linear. Topological. Algebra. 8 (2) (2019), 145-158.
[12] E. Karapinar, Fixed point theory for cyclic weak ϕ-contraction, Appl. Math. Lett. 24 (2011), 822-825.
[13] E. Karapinar, I. Erhan, Best proximity on different type contractions, Appl. Math. Inf. Sci. 5 (2011), 558-569.
[14] W. Kirk, P. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory. 4 (2003), 79-89.
[15] J. Musielak, W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49-65.
[16] J. Musielak, W. Orlicz, Some remarks on modular spaces, Bull. Acad. Polon. Sci. Sr. Sci. Math. Astron. Phys. 7 (1959), 661-668.
[17] H. Nakano, Modular Semi-Ordered Spaces, Tokyo, 1950.
[18] K. Ozkan, U. Gurdal, A. Mutlu, Some fixed point theorems on compact modular metric spaces, Proc. Inst. Math. Mech. Natl. Acad. Sci. Azerb. 46 (2020), 180-188.
[19] H. Rahimpoor, Some contraction fixed point theorems in partially ordered modular metric spaces, Int. J. Nonlinear Anal. Appl. (2023), in press.
[20] H. Rahimpoor, A. Ebadian, M. Eshaghi Gordji, A. Zohri, Some fixed point theorems on modular metric spaces, Acta Univ. Apulensis Math. Inform. 37 (2014), 161-170.
[21] S. Rathee, K. Dhingra, Existence of best proximity and fixed points in Gp-metric spaces, J. Linear. Topological. Algebra. 7 (3) (2018), 155-168.
